Explain it...nope...you'll have to wait till November for that.
Opinions, however.....
My thought is that no. They are not in the Matrix. If you follow the convo with the Architect...you find that 'the One' begins as someone who for some reason cannot assimilate into the Matrix. Their perceptions do not allow them to accept it, and they are able to move beyond it and see the truth, and thus manipulate it. The whole you find out that this whole sad affair is due to one simple thing. All six of the previous persons to be 'the One', failed to fulfil the prophecy.
This whole conflict seems to be a development by the Architect and the Oracle as a means of dealing with 'the One'. The whole...'bargain' if you will, of the two doors, is the way they control 'the One' and thus control humanity. It plays into the very nature of 'the One' by using it to keep humanity in slavery. What Neo did was make the wrong choice that was actually the right choice. Had he walked through the other door, it would have kept humanity under the yoke of the Matrix. Now that he's made the other choice, humanity has the chance to be free.
As to how Neo did what he did.....I'm wondering if it's so far of a fetch that either:
A) part of his 'soul' still resides in the matrix...it maintains a connection to the Matrix and thus can 'enact his will' on it.
B) perhaps he is some way able to utilize his own energy to power his implant, and thus project through there....hey...if we have human batteries, why not a human cell phone?
Of course, this could all be just some idiotic scheme by the matrix to make the people think they've won, so they return to a new form of the matrix, and therefore slavery. If they do that, though, I'm taking my Matrix DVD and putting it on the 'range target' pile.
And no backplot on the asshole that was self-mutilating himself in Zion, the alluded to traitor? What was his deal?
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POTENTIAL SPOILER
Remember the scene where the two Zion soldiers are in the Matrix, but about to leave with a message from the Oracle? Remember when Agent Smith caught one of them and did his presto-changeo routine on him? Remember when said Agent Smith clone put the phone to his ear and actually exited the Matrix? There's your backstory. That dude's Matrix self got 'overwritten' by Agent Smith and thus the 'traitor' is actually Agent Smith acting in the human world.